What happens if the mass of a rigidbody doesn't match to it's volume X density?
It's not that the mass doesn't match  density * volume, it's that the density is defined by
mass / volume.
 Needless to say, the default mass of 1 gram makes most objects very much the opposite of "dense" ;)

To calculate physically accurate values for mass based on measured density of real-world materials, try using the Calculate Mass operator in 3D view > Tool Shelf (T) > Physics > Rigid Body Tools: